Theorems · Theorem · order theory
AbsoluteValue.map_pow
∀ {R : Type u_5} {S : Type u_6} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : PartialOrder S]
(abv : AbsoluteValue R S) [IsDomain S] [Nontrivial R] (a : R) (n : ℕ), abv (a ^ n) = abv a ^ n- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- IsDomainstatement and proof · cited by 2,196
- AbsoluteValuestatement and proof · cited by 363
- MonoidHom.map_powproof · cited by 30
- AbsoluteValue.toMonoidHomproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- ClassGroup.exists_mem_finsetApproxproof · cited by 1
- Rat.AbsoluteValue.equiv_padic_of_boundedproof · cited by 1
- IsAbsoluteValue.abv_powproof · cited by 1
- AbsoluteValue.tendsto_div_one_add_pow_nhds_zeroproof · cited by 1
- IsNonarchimedean.eval_mvPolynomial_leproof · cited by 1
- AbsoluteValue.eval_mvPolynomial_leproof · cited by 1
- Rat.AbsoluteValue.apply_le_sum_digitsproof · cited by 1
- AbsoluteValue.tendsto_div_one_add_pow_nhds_oneproof · cited by 0